Diffraction is frequently used as an analytical technique to characterize compounds or elements. There are situations where a number of materials are analyzed by diffraction techniques and compared to one another in order to determine whether differences in the materials exist. For example, production lots of a compound might be analyzed by diffraction to ensure that the desired material is produced. As another example, a compound might be crystallized under a variety of conditions and the resulting solids analyzed by diffraction to determine if variations in solid form are present. As a third example, an ionizable compound might be reacted with a number of different counterions in an effort to generate a group of different salts. In this case, the solids from the reactions could be analyzed by diffraction and compared to diffraction analyses of the original material and the counterion to help determine whether a salt was formed. It would be useful to have a tool to quickly, easily, and accurately compare diffraction patterns of different materials and sort them into groups of similar patterns.
Hierarchical Cluster Analysis is a statistical method of pattern recognition with wide applicability. Whenever the application is to cluster relatively similar objects together into different groups, then HCA is a common method of choice. The core requirement of HCA is the derivation of a measure of similarity between the objects being clustered. The success of the HCA approach is dependent on the robustness of the measure of similarity chosen. The early implementations of HCA were statistical data analysis where the measure of similarity was the numerical equivalency of the results being analyzed. This has seen wide application for statistical quantitative analysis.
The use of HCA for clustering objects more complex than quantitative values has been limited by the availability of a suitable measure of similarity between the objects to be clustered. The appropriate choice of a measure of similarity is not obvious.
The present invention is directed to overcoming one or more of the above problems and achieving one or more of the above stated goals.